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Periodic Solutions for a Class of Second-Order Ordinary Differential Equations

Author

Listed:
  • S. G. Ji

    (Jilin University)

  • S. Y. Shi

    (Jilin University)

Abstract

This paper is devoted to the study of periodic solutions for a class of second-order ordinary differential equations by utilizing a technique for obtaining solutions to free problems in the calculus of variations originating in the work of Carathéodory (Ref. 1, 1935). The key of this technique is to find some suitable transformation which transfers the periodic solution problem to an equivalent variational problem in which the minimizer is more easily determined. Some applications are presented to illustrate the utility of this technique.

Suggested Citation

  • S. G. Ji & S. Y. Shi, 2006. "Periodic Solutions for a Class of Second-Order Ordinary Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 125-137, July.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:1:d:10.1007_s10957-006-9092-x
    DOI: 10.1007/s10957-006-9092-x
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    References listed on IDEAS

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    1. D. A. Carlson & G. Leitmann, 2004. "An Extension of the Coordinate Transformation Method for Open-Loop Nash Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 27-47, October.
    2. D.A. Carlson, 2002. "An Observation on Two Methods of Obtaining Solutions to Variational Problems," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 345-361, August.
    3. E. J. Dockner & G. Leitmann, 2001. "Coordinate Transformations and Derivation of Open-Loop Nash Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 1-15, July.
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    Cited by:

    1. Z. X. Feng & X. Xu & S. G. Ji, 2009. "Finding the Periodic Solution of Differential Equation via Solving Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 75-86, October.
    2. Nie, Qianqian & Guo, Fei & Wang, Mingwei, 2017. "Generalized Nonsmooth Saddle Point Theorem and its applications on second order Hamiltonian systems," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 741-747.

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